Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 3x + 7$ and $ BC = 2x + 11$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {3x + 7} = {2x + 11}$ Solve for $x$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 3({4}) + 7$ $ BC = 2({4}) + 11$ $ AB = 12 + 7$ $ BC = 8 + 11$ $ AB = 19$ $ BC = 19$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {19} + {19}$ $ AC = 38$